OfficeJet Pro 8600 ink indicator problem

Very frustrating issue: The control panel display on the HP Officejet Pro 8600 printer indicated it was out of the Cyan ink and could not print until empty cartridge was replaced. NOTE: At this same time, it showed that it still had about 30% ink left (estimating) for Magenta, Yellow, and Black, but they did NOT indicate they were almost empty!

Trip to store to get the Cyan ink cartridge. As soon as the new cartridge was put in, the control panel display THEN showed the Yellow ink was empty, and it would not print until empty cartridge was replaced!

(HOW could the Yellow cartridge go from having ink, to completely EMPTY, just from changing the Cyan cartridge?)

Also NOTE that the Magenta and Black still showed ink and did NOT indicate they were almost empty!

Another trip to the store to get a new Yellow cartridge. Guess what? As soon as the Yellow cartridge was installed, the control panel display THEN showed that the Magenta ink cartridge was empty, and would not print until empty cartridge is replaced!

WHAT?! Again, how did the Magenta go from having ink, to being empty, just from changing the Yellow cartridge?

Talk about frustrating! Have not been able to go out and buy the new Magenta ink cartridge yet. Once that is replaced, then what?? Is the Black ink going to mysteriously show empty also?

If all colors were empty, WHY NOT indicate that at the same time? Rather than 'saying' they had ink until another cartridge was replaced?

Can someone help with this? This is actually our mom's printer, but it bothered me so much, I wanted to see if I could find out anything for her. Thanks!